A052901 Periodic with period 3: a(3n)=3, a(3n+1)=a(3n+2)=2.

3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Continued fraction expansion of (15 + sqrt(365))/10 = A176979. - Klaus Brockhaus, Apr 30 2010

First differences of A047390. - Tom Edgar, Jul 17 2014

Also decimal expansion of 322/999. - Nicolas Bělohoubek, Nov 11 2021

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 878
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A176979 (decimal expansion of (15+sqrt(365))/10).

Cf. A208131 (partial products).

Programs

Haskell

a052901 n = a052901_list !! n
a052901_list = cycle [3,2,2]  -- Reinhard Zumkeller, Apr 08 2012

Maple

spec := [S,{S=Union(Sequence(Z),Sequence(Z),Sequence(Prod(Z,Z,Z)))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

PadRight[{},110,{3,2,2}] (* Harvey P. Dale, Mar 19 2013 *)
LinearRecurrence[{0, 0, 1},{3, 2, 2},105] (* Ray Chandler, Aug 25 2015 *)

PARI

Vec((2*x^2+2*x+3)/(1-x^3)+O(x^99)) \\ Charles R Greathouse IV, Apr 08 2012

Formula

G.f.: (2*x^2 + 2*x + 3)/(1-x^3).

a(n) = Sum((1/3)*(2*alpha^2 + 3*alpha + 2)*alpha^(-1-n), where alpha = RootOf(-1+x^3)).

a(n) = ceiling(7*(n+1)/3) - ceiling(7*n/3). - Tom Edgar, Jul 17 2014

From Nicolas Bělohoubek, Nov 11 2021: (Start)

a(n) = 12/(a(n-2)*a(n-1)).

a(n) = 7 - a(n-2) - a(n-1). See also A069705 or A144437. (End)

Extensions

More terms from James Sellers, Jun 06 2000